# LOQA: Learning with Opponent Q-Learning Awareness

arXiv: https://arxiv.org/abs/2405.01035 · HTML: https://mlsanity.com/paper/2405.01035/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 12 of its 20 references that are in the map.
- First posted on arXiv 2 May 2024.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 12 of 12)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Learning with Opponent-Learning Awareness](https://mlsanity.com/paper/1709.04326/) (2017)
- [Continuous Adaptation via Meta-Learning in Nonstationary and Competitive Environments](https://mlsanity.com/paper/1710.03641/) (2017)
- [Stable Opponent Shaping in Differentiable Games](https://mlsanity.com/paper/1811.08469/) (2018)
- [Maintaining cooperation in complex social dilemmas using deep reinforcement learning](https://mlsanity.com/paper/1707.01068/) (2017)
- [DiCE: The Infinitely Differentiable Monte-Carlo Estimator](https://mlsanity.com/paper/1802.05098/) (2018)
- [A Policy Gradient Algorithm for Learning to Learn in Multiagent Reinforcement Learning](https://mlsanity.com/paper/2011.00382/) (2020)
- [Loaded DiCE: Trading off Bias and Variance in Any-Order Score Function Estimators for Reinforcement Learning](https://mlsanity.com/paper/1909.10549/) (2019)
- [Meta-Value Learning: a General Framework for Learning with Learning Awareness](https://mlsanity.com/paper/2307.08863/) (2023)
- [Best Response Shaping](https://mlsanity.com/paper/2404.06519/) (2024)

## Built on by (most cited first, 8 of 8)

- [Advantage Alignment Algorithms](https://mlsanity.com/paper/2406.14662/) (2024)
- [Multi-agent cooperation through learning-aware policy gradients](https://mlsanity.com/paper/2410.18636/) (2024)
- [Reciprocal Reward Influence Encourages Cooperation From Self-Interested Agents](https://mlsanity.com/paper/2406.01641/) (2024)
- [Learning Robust Social Strategies with Large Language Models](https://mlsanity.com/paper/2511.19405/) (2025)
- [The challenge of hidden gifts in multi-agent reinforcement learning](https://mlsanity.com/paper/2505.20579/) (2025)
- [Multi-agent cooperation through in-context co-player inference](https://mlsanity.com/paper/2602.16301/) (2026)
- [Towards Sustainable Investment Policies Informed by Opponent Shaping](https://mlsanity.com/paper/2602.11829/) (2026)
- [Differentiable Belief-based Opponent Shaping](https://mlsanity.com/paper/2605.29042/) (2026)

## Abstract (arXiv)

In various real-world scenarios, interactions among agents often resemble the dynamics of general-sum games, where each agent strives to optimize its own utility. Despite the ubiquitous relevance of such settings, decentralized machine learning algorithms have struggled to find equilibria that maximize individual utility while preserving social welfare. In this paper we introduce Learning with Opponent Q-Learning Awareness (LOQA), a novel, decentralized reinforcement learning algorithm tailored to optimizing an agent's individual utility while fostering cooperation among adversaries in partially competitive environments. LOQA assumes the opponent samples actions proportionally to their action-value function Q. Experimental results demonstrate the effectiveness of LOQA at achieving state-of-the-art performance in benchmark scenarios such as the Iterated Prisoner's Dilemma and the Coin Game. LOQA achieves these outcomes with a significantly reduced computational footprint, making it a promising approach for practical multi-agent applications.